Question

Paco uses a spinner to select a number from 1 through 5, each with equal probability. Manu uses a different spinner to select a number from 1 through 10, each with equal probability. What is the probability that the product of Manu's number and Paco's number is less than 30?

Answer 1

Answer:
`(41)/(50)`

Explanation:

Given : The number of sections in Paco's spinner =5

The number of sections in Manu's spinner =10

Now, if both spin together , the total number of possible outcomes :-

`5*10=50`

The outcomes when the product is more than 30 :-

(5,6), (5,7), (5,8), (5,9), (5, 10), (4,8), (4,9), (4, 10), (3,10)

The number of favorable outcomes for the product of Manu's number and Paco's number is less than 30 :-

`50-9=41`

Now, the probability that the product of Manu's number and Paco's number is less than 30 :-

`=(41)/(50)`

Hence, the probability that the product of Manu's number and Paco's number is less than 30
`=(41)/(50)`.

Answer 2

There are 5 x 10 = 50 different outcomes.

Of them only 3x10, 4x10, 4x9, 4x8, 5x10, 5x9, 5x8, 5x7 and 5x6 are greater or equal than 30. Those are 9 possibilities.

Then 50 - 9 = 41 are the possibilities that the product of the two numbers is less than 30.

The probalility, then, is 41/50 = 0.82