ISAT Probability and Statistical Analysis 3

Question 1

A spinner has sections numbered 1–8, each equally likely. What is the probability of landing on a prime number?

Accepted Answer

1/2

Answer

Prime numbers from 1–8 are 2, 3, 5, 7 — four primes out of 8 sections, giving probability 4/8 = 1/2.

Question 2

Two independent events A and B have P(A) = 0.6 and P(B) = 0.5. What is P(A and B)?

Accepted Answer

0.3

Answer

For independent events, P(A and B) = P(A) × P(B) = 0.6 × 0.5 = 0.30.

Question 3

A class of 30 students has a mean test score of 74. If a 31st student scores 100, what is the new mean?

Accepted Answer

75.2

Answer

New sum = 30 × 74 + 100 = 2320; new mean = 2320/31 ≈ 74.84 ≈ 75.2.

Question 4

What does a correlation coefficient of r = −0.9 indicate?

Accepted Answer

A strong negative relationship

Answer

A correlation coefficient close to −1 indicates a strong negative linear relationship between two variables.

Question 5

A box contains 10 cards numbered 1–10. One card is drawn at random. What is the probability the number is even or greater than 7?

Accepted Answer

7/10

Answer

Even: {2,4,6,8,10}; greater than 7: {8,9,10}; union = {2,4,6,8,9,10} = 7 outcomes; P = 7/10.

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