A retail company offers a \"scratch off\" promotion. Upon entering the store, yo

Question

A retail company offers a "scratch off" promotion. Upon entering the store, you are given a card. When you pay, you may scratch off the coating. The company advertises 30% of the cards are winners and have immediate cashback savings of $15 (the others offer $2 off any future purchase of coffee in the cafe). You aren't sure the percentage is really 30% winners. Complete parts a through d below. The first time you shop there, you get the coffee coupon. You try again, and again get the coffee coupon. Do two failures in a row convince you that the true fraction of winners isn't 30%? Explain.

Explanation / Answer

Probability of Losing twice in a row=0.7*0.7=0.49=49%

As the winning chance is 30%, Which gives approximately 3 in every 10 or 1 in every 3.33

Hence if I had gone to the shop at least 4 times and I always won a coffee coupon,I wouldnt be convinced that the fraction isn't 30%.

Hence

No,because the chance of losing twice in a row is 49%, which is not unusual.

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