NCUK Probability

A box holds 4 blue beads and 5 green beads. One bead is taken and not replaced.

2 yellow beads are then added to the box and a second bead is taken.

Find the probability that neither bead is blue.

• $\frac{2}{5}$

• 0

• 3

• $\frac{1}{3}$

A student plays two games of badminton. The probability that she wins the first game is 0.65. If she wins the first game, the probability that she wins the second is 0.8. If she does not win the first game, the probability that she wins the second is 0.4. Find the probability that she wins exactly one game.

• 0.27

• 0.34

• 0.18

• 0.91

The probability it rains on any day is 0.6. Find the probability that it rains:

a) on both days.

b) on exactly one day.

• a) 0.43 b) 0.67

• a) 0.36 b) 0.48

• a) 0.32 b) 0.98

• a) 0.41 b) 0.11

X, Y and Z are three independent events. Event X occurs with probability 0.39, event Y occurs with probability 0.53 and event Z occurs with probability 0.08.

Find the probability that none of the events X, Y or Z occurs.

Give your answer to 3 significant figures.

• 0.263764

• 0.26

• 0.264

• 0.263

A box holds 3 red beads and 2 blue beads. Two beads are drawn, one after the other and with no replacement.

Find the probability that both beads will be of the same colour.

• $\frac{1}{2}$

• $\frac{9}{2}$

• $\frac{4}{7}$

• $\frac{2}{5}$

A bag holds 5 red sweets and 4 blue sweets. Three sweets are drawn from the bag, one after other and with no replacement.

a) Find the probability that all three sweets are red.

After the three sweets have been taken, 7 green sweets are added to the bag. Another sweet is then taken.

b) Find the probability it is not green.

• $\left(a\right)\ \frac{5}{42}\ \left(\approx0.12\right)\ \left(b\right)\frac{1}{3}\ \left(\approx0.333\right)$

• $\left(a\right)\ \frac{1}{3}\ \left(\approx0.333\right)\ \left(b\right)\frac{2}{7}\ \left(\approx0.286\right)$

• $\left(a\right)\ \frac{4}{17}\ \left(\approx0.24\right)\ \left(b\right)\frac{2}{13}\ \left(\approx0.154\right)$

• $\left(a\right)\ \frac{5}{42}\ \left(\approx0.12\right)\ \left(b\right)\frac{6}{13}\ \left(\approx0.016\right)$

A box holds 7 red beads, 4 blue beads and 3 green beads.

Three beads are drawn at random, one after the other with no replacement.

Find the probability that the first two beads are blue and the third bead is green.

• $\frac{3}{182}$

• $\frac{2}{117}$

• $\frac{7}{213}$

• $\frac{1}{543}$

The probability that it rains on a given day is 3c - 2. The probability that it does not rain is 2c - 1. Find the value of c and the probability that it rains on two consecutive days.

• $c\ =\ \frac{2}{5},\ 0.16$

• $c\ =\ \frac{2}{5},\ 0.46$

• $c\ =\ \frac{4}{5},\ 0.32$

• $c\ =\ \frac{4}{5},\ 0.16$

Three letters are selected, one after the other and with no replacement, from the word LOCOMOTION.

Find the probability that none of them is the letter 'O'.

• $\frac{2}{3}$

• $\frac{1}{6}$

• $\frac{1}{7}$

• $\frac{6}{7}$

A student plays two games of tennis. The probability that he wins the first game is  $\frac{3}{5}$ . If he wins the first game the probability that he wins the second is  $\frac{2}{3}$ . If he does not win the first game, the probability that he wins the second is  $\frac{7}{10}$ . Draw a label a tree diagram. Find the probability that he wins exactly one game.

•  $\frac{12}{25}$  (0.48)

•  $\frac{4}{25}$  (0.16)

•  $\frac{3}{25}$  (0.12)

•  $\frac{21}{25}$  (0.84)