Question

cards marked with numbers 4 to 99 are placed in a box and mixed thoroughly . One card is drawn from this box . Find the probability that the number on the card is : a perfect square
A multiple of 7
A prime no less than 30
A perfect square between 91 to 99​

Answer 1

Answer:

perfect square=0/99

prime=8/99

multiple=13/99

Step-by-step explanation:

Answer 2

a. probability of a perfect square =  $\frac{1}{12}$ = 8.33%

b. probability of a multiple of 7 =  $\frac{7}{48}$ =  14.58%

c. probability of prime number less than 30 = $\frac{5}{48}$ = 10.41%

d. a perfect square between 91 to 99 =  $\frac{0}{96}$ = 0%

Step-by-step explanation:

Cards marked with number 4 to 99.

Total number of cards placed in a box = 96

If repetition is allowed

The numbers that are perfect square = 4, 9 , 16, 25, 36, 49, 64, 81,

Total 8 cards of these numbers that are perfect square.

So the probability that the number on the card is a perfect square = $\frac{8}{96}$ = $\frac{1}{12}$

Number of cards that are multiple of 7 = 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98

There are total 14 cards that has numbers of multiple of 7.

So the probability that the number on the card is a multiple of 7 = $\frac{14}{96}$ = $\frac{7}{48}$

Prime numbers less than 30 = 2, 3, 5, 7, 11, 13, 17, 19, 23, 29

There are total 10 cards that has prime numbers less than 30.

So the probability that the number on the card is a prime number less than 30 = $\frac{10}{96}=\frac{5}{48}$

Numbers that are perfect square between 91 to 99 = 0

So the probability that the number on the card a perfect square between 91 to 99 = $\frac{0}{96}$

a. probability of a perfect square =  $\frac{1}{12}$ = 8.33%

b. probability of a multiple of 7 =  $\frac{7}{48}$ =  14.58%

c. probability of prime number less than 30 = $\frac{5}{48}$ = 10.41%

d. a perfect square between 91 to 99 =  $\frac{0}{96}$ = 0%

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