Jayanti throws a pair of dice and records the product of the numbers appearing on the dice. Pihu throws 1 dice and records the squares the number that appears on it. Who has the better chance of getting the number 36?

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Pihu has the better chance of getting the number 36.

Jayanti has the better chance of getting the number 36.

Pihu does not have the better chance of getting the number 36.

Both Pihu and Jayanti has the better chance of getting the number 36.

answer is A.

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Detailed Solution

Given that, Jayanti throws a pair of dice and records the product of the numbers appearing on the dice.
We know that, a die has 6 faces marked as 1, 2, 3, 4, 5, and 6.
If we throw two dices, then the set of possible outcomes are {(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)}.
Therefore, total no. of possible outcomes when 2 dice are thrown = 6 x 6 = 36.
Pihu throws 1 dice and records the square of the number that appears on it.
If we throw one die, then the possible outcomes are as 1, 2, 3, 4, 5 and 6.
We already know that,
Required probability =

\frac{Number of favorable outcomes}{Total number of outcomes}

.
For Jayanti, as she throws a pair of dice, the total Number of possible outcomes = 36
Let us assume, E = Event of getting the product of the numbers appearing on the dice.
Favorable outcomes for Jayanti (product of the numbers appearing on the dice) = (6, 6).
So, number of favorable outcomes = 1.
We know,
Probability, P(E) =

\frac{Number of favorable outcomes}{Total number of outcomes}

.
By substituting the values, we get,

P (E) = 136

So, the probability of getting the product of the numbers appearing on the dice as 36 is P(E) = 1/36
For Pihu, as she throws a single dice, total Number of possible outcomes = 6
Let us assume S = Event of getting the square of the number that appears on it as 36.
There is only one possible outcome 6 of which square is 36.
So, number of favorable outcomes = 1
Probability, P(S) =

\frac{Number of favorable outcomes}{Total number of outcomes}

.
By substituting the values, we get,

P (S) = 16

So, the probability of getting square of the number that appears on it as 36 is P(S) = ⅙.
As we can observe, P(S) > P(E).
Hence, Pihu has a better chance of getting the number 36.
The correct option is (1).

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