Throw money five times. Let's denote the number with the coat of arms by "y". Write the distribution law of "y" and draw a graph.

Question

help me with this one

Answer 1

If you mean toss a coin 5 times then there is an equal probability that the coin will land heads or tails up. I assume that the coat of arms is a tail. Anyway, we call it y (yes) and not-y (or no or "n") if it's the other side. The probability is p=½ for either of these outcomes.

We can represent the probability binomially:

All the outcomes are represented by 

(½+½)⁵=½⁵+5×½⁴×½+10×½³×½²+10×½²×½³+5×½×½⁴+½⁵=1.

This can be written (½+½)⁵=(1/32)(1+5+10+10+5+1). Each term represents the probability of:

All y's, 4 y's, 3 y's, 2 y's, 1 y, No y's. The coefficients are given by 5!/(n!(5-n)!) where n is the number of y's.

Probability of exactly n y's in 5 throws is P(n)=(1/32)(5!/(n!(5-n)!)).

This can be graphed with n as the horizontal axis and P as the vertical axis:

The scale of the P-axis is 1=1/32, so, for example, 5 represents a probability of 5/32 or about 0.16.

Part of the curve shown fits the 6 probabilities exactly.