g you are playing a game in which you flip 3 fair coins. it costs $1 to play the game, which must be subtracted from your winnings. Calculate the expected value for the game. If all coins show the same (all heads or all tails) you win $7, otherwise you lose your $1. The expected value of the game is

Expected value of the game is $1.75

Step-by-step explanation:

The probability of getting a head or a tail on flipping a coin is 1/2 and so the probability of winning is 1/2 as we need all heads or all tails . There are 3 fair coins so the expected value of winning is given by =

P(1st coin =x =head)= 1/2

P(2nd coin =x =head)= 1/2

P(3rd coin =x =head)= 1/2

P(1st coin =x =tail)= 1/2

P(2nd coin =x =tail)= 1/2

P(3rd coin =x =tail)= 1/2

E(X= win) = ∑xP(x)=  (1/2)³+(1/2)³= 1/8 + 1/8= 2/8

Expected value of winning the game is $ 7*2/8= 14/8=$ 1.75

$ 1.75- $1= $ 0.75

$ 0.75 (8) = $ 6

This means that for a total of $ 8  he gets $ 6.

arithmetic sequence

step-by-step explanation:

given that a sequence has terms as

19, 15, 11,

this is represented on a graph

the pattern indicates that the sequence is an arithmetic sequence with i term

a=19 and common difference d =-4

any general term

thus the sequence is reduced by 4 for each successive term starting from 1 and nth term is

24-5n.

first negative term would start after 5th term

5th term =24-25< 0

from 5th term onwards the sequence would be negative.

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