# Answer to Question #351048 in Statistics and Probability for Bob

Question #351048

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 following events?

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.

1
2022-06-28T03:15:05-0400

(a) Since the probability of the set of all possible outcomes "P(\\Omega)=1," then

"P(Brown)+P(Red)+P(Yellow)+P(Green)\\\\+P(Orange)+P(Tan)=P(\\Omega)=1"

hence "P(Tan)=1-0.3-0.2-0.2-0.1-0.1=0.1."

(b)

i. "P(Brown)+P(Red)=0.3+0.2=0.5."

ii. "P(\\Omega)-P(Yellow)=1-0.2=0.8."

iii.

"P(\\Omega)-P(Orange\\ or\\ Tan)=1-P(Orange)-P(Tan)=1-0.1-0.1=0.8."

iv. "P( brown\\ or\\ red\\ or\\ yellow\\ or\\ green\\ or\\ orange\\ or\\ tan)=P(\\Omega)=1."

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