Question #351005

4. QUESTION:

M&M sweets are of varying colours and the diﬀerent colours occur in diﬀerent proportions. The table below gives the probability that a randomly chosen M&M has each colour, but the value for tan candies is missing.

Colour Brown Red Yellow Green Orange Tan

Probability 0.3 0.2 0.2 0.1 0.1 ?

(a) What value must the missing probability be?

(b) You draw an M&M at random from a packet. What is the probability of each of the followingevents?

i. You get a brown one or a red one.

ii. You don’t get a yellow one.

iii. You don’t get either an orange one or a tan one.

iv. You get one that is brown or red or yellow or green or orange or tan.

Expert's answer

Since all the probabilities add up to 1, the missing probability of tan colour is

"1 - (0.3 + 0.2 + 0.2 + 0.1 + 0.1) = 1 - 0.9 = 0.1."

**(i)** Probability of drawing a brown one or a red one by the addition rule is

"0.3 + 0.2 = 0.5."

**(ii)** Probability of not drawing a yellow one is

"1 - 0.2 = 0.8."

**(iii)** Probability of not drawing either an orange or a tan one is

"1 - (0.1 + 0.1) = 1 - 0.2 = 0.8."

**(iv)** Probability of drawing one that is brown or red or yellow or green or orange or tan is by the additional rule is

"0.3 + 0.2 + 0.2 + 0.1 + 0.1 + 0.1 = 1."

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