Answer to Question #351005 in Statistics and Probability for EDD

Question

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.

Answer 1

(a)

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

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

(b)

(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

$0.3 + 0.2 + 0.2 + 0.1 + 0.1 + 0.1 = 1.$