Apoorv throws two dice once and computes the product of the numbers appearing on the dice. Peehu throws one die and squares the number that appears on it. Who has the better chance of getting the number 36? Why?
Step 1: Understand Peehu's case
Peehu throws only one die. A die has six faces: 1, 2, 3, 4, 5, 6.
She squares the number that comes. To get 36, she must have:
\(6^2 = 36\).
So Peehu gets 36 only when she rolls a 6.
Probability = \(\dfrac{1}{6}\), because only 1 favorable outcome (rolling a 6) out of 6 total outcomes.
Step 2: Understand Apoorv's case
Apoorv throws two dice together. Each die has 6 faces, so total outcomes = \(6 \times 6 = 36\).
He multiplies the two numbers. We want the product to be 36.
Let’s check possible pairs:
So only one favorable outcome exists: (6, 6).
Probability = \(\dfrac{1}{36}\).
Step 3: Compare probabilities
Peehu: \(\dfrac{1}{6}\)
Apoorv: \(\dfrac{1}{36}\)
Since \(\dfrac{1}{6} > \dfrac{1}{36}\), Peehu has a higher chance.
Final Answer: Peehu has the better chance of getting 36.