Photo AI

The probabilities of events A, B and C are related, as shown in the Venn diagram below - AQA - A-Level Maths Mechanics - Question 10 - 2020 - Paper 3

Question 10

The probabilities of events A, B and C are related, as shown in the Venn diagram below. Find the value of x. Circle your answer. A: 0.12 B: 0.05 C: 0.18 0.30 0.24

Worked Solution & Example Answer:The probabilities of events A, B and C are related, as shown in the Venn diagram below - AQA - A-Level Maths Mechanics - Question 10 - 2020 - Paper 3

Step 1

Find the total probability in the Venn diagram

96%

114 rated

Answer

To find the value of x, we need to ensure that the total probability for all events A, B, and C, including the overlaps, equals 1. The total sum of probabilities provided is:

$ext{Total} = 0.12 + 0.05 + 0.18 + 0.30 + 0.24 + x$

So we write the equation:

$0.12 + 0.05 + 0.18 + 0.30 + 0.24 + x = 1$

Calculating the sum of the known probabilities:

$0.12 + 0.05 + 0.18 + 0.30 + 0.24 = 0.89$

Step 2

Solve for x

99%

104 rated

Answer

Now we substitute this sum back into our equation:

$0.89 + x = 1$

To isolate x, subtract 0.89 from both sides:

$x = 1 - 0.89$

Thus:

$x = 0.11$

Step 3

Circle the correct answer

96%

101 rated

Answer

The value of x is 0.11. Therefore, we circle the answer 0.11.

Join the A-Level students using SimpleStudy...

97% of Students

Report Improved Results

98% of Students

Recommend to friends

100,000+

Students Supported

1 Million+

Questions answered

;