Question

: Tablet computers have become very popular and fill a gap between smartphones and PCs. A recent survey of tablets owners indicated that 70% use the device to play games, 44% use the device to access bank accounts, and 30% do both (play games and access bank accounts). a. David is a tablet owner. What is the probability that he uses the device to play games or to access bank accounts. b. What is the probability that David does not use the device to play games nor to access bank accounts? c. What is the probability that David uses the device to play games only. d. Ten tablet owners are selected at random. What is the probability that at most three of them use their device to play games only?

Answer 1

let A and B are the event of play games and access bank accounts

a) probability that he uses the device to play games or to access bank accounts

=P(A u B)=P(A)+P(B)-P(A n B)=0.7+0.44-0.3=0.84

b) probability that David does not use the device to play games nor to access bank accounts

=1-P(A u B)=1-0.84 =0.16

c)

probability that David uses the device to play games only =P(A)-P(A n B)=0.7-0.3=0.40

d) probability that at most three of them use their device to play games only

=P(X<=3)=P(X=0)+P(X=1)+P(X=2)+P(X=3)

=¹⁰C₀(0.40)⁰(0.6)¹⁰+¹⁰C₁(0.40)¹(0.6)⁹+¹⁰C₂(0.40)²(0.6)⁸+¹⁰C₃(0.40)³(0.6)⁷=0.3823