4.4.1 Probability (A-level only)

Medium Hard

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99

Question 16

The Venn diagram shows the probabilities associated with three events $X$ , $Y\,$ and $Z$ , representing students choosing to study different languages. The probability of students studying only $X\,$ is 0.15, only $Y\,$ is 0.2, and only $Z\,$ is 0.4. The intersection $\cap Y\,$ is $q\,$ and $\cap Z\,$ is $p$ . Events $X\,$ and $Z\,$ are disjoint. The probability of studying none of these languages is $r$ .

Write down the two events that are mutually exclusive.

[1]

Given that $P (Y ∣ Z) = 0.2$ , find the value of $p$ .

[2]

Given also that $X\,$ and $Y\,$ are independent, find the values of $q\,$ and $r$ .

[4]

4.4.1 Probability (A-level only) Questions

A Level
Maths
4.4.1 Probability (A-level only)

A Level
Maths CCEA
Question bank