Question

A die is thrown twice. What is the probability that there is an odd number on the first throw and a prime number on the second throw?

a) 1/6
b) 1/4
c) 1/3
d) 1/2​

Answer 1

Answer:

An unbiased die is thrown twice. Let the event A be 'odd number on the first throw' and B the event 'odd number on the second throw'. Check the independence of the events A and B. Number of elements (outcomes) of the above example space is 6 x 6 = 36.

Answer 2

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Given:

A die is thrown twice.

To find:

Probability of getting an odd number on first throw and prime number on second throw = ?

Solution:

Let S be the sample space of die thrown twice

S = { ( 1,1 ) ( 1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6) }

n(S) = 36

Let A be the event of getting odd on first throw and prime number in second throw

1,3,5 are the odd numbers expected in dice

2,3,5 are the prime numbers expected in dice

B = { ( 1,2 ) (1,3) (1,5)

(3,2) (3,3) (3,5)

(5,2) (5,3) (5,5) }

n(A) = 9

Probability of A = n(A) / n(S)

P(A) = 9/36

P(A) = 1/4

Answer:

Option D : 1/4

Thus, probability that there is an odd number on the first throw and a prime number on the second row is 1/4

Knowledge booster:

⟹ Probability of an event is equal to number of sample points in event upon number of sample points in S

⟹ As dice is thrown once, sample space will be equal (1, 2,3,4,5,6)

⟹ Sample space can be denoted as S or omega

⟹ If a dice is thrown twice, then (x, y) x is the outcome in first throw and y is the outcome in second throw

⟹ Try to examine and solve more such questions to get good hold on it