One of four main blood types can be found in a human body. They are known as A, B, AB and O. Each blood type can be further classified as either a Rhesus positive (+) or Rhesus negative (−). For example, a possible combination is blood type O and Rhesus negative which is written as O^-. The data below shows the distribution of the blood types and Rhesus types of given blood type for a Blood Donation Center recorded (in percentages) for the year 2023. Blood Group Rhesus Factor Number of Persons (in %) --- --- --- O O^- x O O^+ 30 A A^- 8 A A^+ 24 B B^- 6 B B^+ 18 AB AB^- 1 AB AB^+ 3 (i) Find the value of x. (ii) Find the probability that a randomly selected person has a Rhesus negative blood type. (iii) (A) What is the probability that the person selected from the record is Rhesus positive but neither blood type A nor B? (iii) (B) People with blood type AB positive (AB^+) are known as the universal recipient and with blood type O negative (O^-) are known as universal donor. Find the probability of a selected person to be neither universal recipient nor universal donor.

MathsCBSE Class 10 · Basic · Sample paper, session 2025-26 · 4 marks · Case-based

CBSE Class 10 Mathematics Basic sample paper 2025-26: question 38

From the official CBSE sample question paper for 2025-26, section E, question 38, for 4 marks. Try it first; the hints and our step-by-step solution are below.

Q38 · 4 marks · Case-basedCompetency-basedProbability

One of four main blood types can be found in a human body. They are known as A, B, AB and O. Each blood type can be further classified as either a Rhesus positive (+) or Rhesus negative (−). For example, a possible combination is blood type O and Rhesus negative which is written as O $^{-}$ .

The data below shows the distribution of the blood types and Rhesus types of given blood type for a Blood Donation Center recorded (in percentages) for the year 2023.

Blood Group	Rhesus Factor	Number of Persons (in %)
O	O $^{-}$	$x$
O	O $^{+}$	30
A	A $^{-}$	8
A	A $^{+}$	24
B	B $^{-}$	6
B	B $^{+}$	18
AB	AB $^{-}$	1
AB	AB $^{+}$	3

(i)
Find the value of $x$ .
1 mark
(ii)
Find the probability that a randomly selected person has a Rhesus negative blood type.
1 mark
(iii)
(A) What is the probability that the person selected from the record is Rhesus positive but neither blood type A nor B?
2 marks
OR
(iii)
(B) People with blood type AB positive (AB $^{+}$ ) are known as the universal recipient and with blood type O negative (O $^{-}$ ) are known as universal donor. Find the probability of a selected person to be neither universal recipient nor universal donor.
2 marks

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2025-26.

Hints

Open one hint at a time and try again before the next.

Hint 1

All the percentages together must add up to 100.

Hint 2

For probability, use (percentage in the favourable group)/100.

Hint 3

In (iii)(B), use the complement: find P(universal recipient or donor) first, then subtract it from 1.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

(i) The percentages total 100, so $x = 100 - (30 + 8 + 24 + 6 + 18 + 1 + 3) = 100 - 90 = 10$ .
1 mark
(ii) Rhesus negative persons: $O^{-} + A^{-} + B^{-} + A B^{-} = 10 + 8 + 6 + 1 = 25$ (per cent).
So $P (Rh^{-}) = \frac{25}{100} = \frac{1}{4}$ .
1 mark
(iii)(A) Rhesus positive but neither A nor B means $O^{+}$ or $A B^{+}$ , which is $30 + 3 = 33$ (per cent).
1 mark
(iii)(A) Required probability $= \frac{33}{100}$
1 mark
(iii)(B) Universal recipients ( $A B^{+}$ ) $= 3$ and universal donors ( $O^{-}$ ) $= 10$ , giving 13 in total.
$P (neither) = 1 - \frac{3 + 10}{100} = 1 - \frac{13}{100}$
1½ marks
(iii)(B) $= \frac{87}{100}$
½ mark

Answer: (i) x = 10; (ii) 1/4; (iii)(A) 33/100; (iii)(B) 87/100

Where the marks are

(i) x = 10 (1 mark)
(ii) P(Rh negative) = 25/100 = 1/4 (1 mark)
(iii)(A) Identifies $O^{+}$ and $A B^{+}$ , total 33 (1 mark); probability 33/100 (1 mark)
(iii)(B) Uses $1 - \frac{3 + 10}{100}$ (1½ marks); gets 87/100 (½ mark)

Revise the chapter

Chapter: Probability (notes, formulas, where marks are lost and every past question)
Topic: Properties of Probability and Complementary Events

Practise this chapterBoard-style questions from Probability, one at a time, marked against the answer key and marking points.Back to the full paperSample paper 2025-26 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic sample paper 2025-26: question 38

Hints

Step-by-step solution

Revise the chapter

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