State true or false.

The probability of getting a prime number is the same as that of a composite number in a throw of a dice.

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

True

False

answer is B.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Given that, the probability of getting a prime number is the same as that of a composite number in a throw of a dice.
Observe that, a dice is rolled, the six possible outcomes are

1, 2, 3, 4, 5, 6

.
Therefore, the composite numbers in a dice are

4, 6

.
Number of composite numbers = 2.
The formula for the probability is,
Probability of an event E

= \frac{n (E)}{n (S)}

where n(E) = number of favourable outcomes and
n(S) = total number of outcomes.
Calculate the probability of occurrence of composite numbers.

​ ​ ​ ​ Total number of composite numbers Total numbers = 26 = 13

The prime numbers in a dice are 2, 3, 5.
Apply formula and calculate the probability of occurrence of prime numbers,
Probability of occurrence of prime numbers is given by,

= \frac{3}{6}

= \frac{1}{2}

13 ≠ 12

The correct statement is the probability of getting a prime number is the not the same as that of a composite number in a throw of a dice.
Hence, the statement is false.
Therefore, option 2 is correct.

Watch 3-min video & get full concept clarity