Methods2025 NHT Exam 1 · Q6Tech-free4 marks

High jumper attempts: probability distribution and conditional probability

A high jumper has up to three attempts to jump over a bar at a specific height.

Once one attempt is successful, the high jumper does not make another attempt at this height.

At this height, let

$\Pr(A) = 0.6$ and

a.i.

Let $N$ be a discrete random variable representing the number of attempts the high jumper makes at this height.

Complete the table below for the probability distribution of $N$ .

| $n$ | 1 | 2 | 3 | |---|---|---|---| | $\Pr(N = n)$ | 0.6 | | |

A table with a row of values n = 1, 2, 3 and a row Pr(N = n) with 0.6 given for n = 1 and blank cells for n = 2 and n = 3.

1 mark

Hints, answer checking and worked solutions come with a Season Pass.

a.ii.

Find $\operatorname{E}(N)$ , the mean number of attempts the high jumper makes at this height.

1 mark

Hints, answer checking and worked solutions come with a Season Pass.

The high jumper was not successful on the first attempt at this height.

Find $\Pr(C|B')$ , given that the high jumper has a 0.7 probability of making a successful jump on either their second or third attempt.

2 marks

Hints, answer checking and worked solutions come with a Season Pass.

Methods2025 NHT Exam 1 · Q6Tech-free4 marks

A high jumper has up to three attempts to jump over a bar at a specific height.

Once one attempt is successful, the high jumper does not make another attempt at this height.

At this height, let

$\Pr(A) = 0.6$ and

a.i.

Let $N$ be a discrete random variable representing the number of attempts the high jumper makes at this height.

Complete the table below for the probability distribution of $N$ .

| $n$ | 1 | 2 | 3 | |---|---|---|---| | $\Pr(N = n)$ | 0.6 | | |

A table with a row of values n = 1, 2, 3 and a row Pr(N = n) with 0.6 given for n = 1 and blank cells for n = 2 and n = 3.

1 mark

Hints, answer checking and worked solutions come with a Season Pass.

a.ii.

Find $\operatorname{E}(N)$ , the mean number of attempts the high jumper makes at this height.

1 mark

Hints, answer checking and worked solutions come with a Season Pass.

The high jumper was not successful on the first attempt at this height.

Find $\Pr(C|B')$ , given that the high jumper has a 0.7 probability of making a successful jump on either their second or third attempt.

2 marks

Hints, answer checking and worked solutions come with a Season Pass.